Erciyes University - Info Package

Course unit title	Level of course unit	Course unit code	Type of course unit	Semester of course unit	Local credit	ECTS credit	Syllabus
DIFFERENTIABLE MANIFOLDS-I	Second cycle	MAT 565		1	7.50	7.50	Print

Description of course unit

Prerequisites and course requisities	NO
Language of instruction	Turkish
Coordinator	Assoc.Prof. Dr. NAZMİYE ALEMDAR
Lecturer(s)	Assoc.Prof. Dr. NAZMİYE ALEMDAR
Teaching assitant(s)	NO
Mode of delivery	Face to face
Course objective	The aim of this course is to give basic concepts and theorems of Differentiable Manifolds.
Course description	Topological Spaces, Contininuous Function, Differentiable Manifold, Differentiable Function, The Induced Topology on a Manifold, Differentiable Varieties, Grassman Manifolds, Manifold Structure on a Topological Space, Properties of Induced Topolgy, Topological Restrictions on a Manifold, Partial Differentiation, Tangent Vectors, İmmersions, Submanifolds

Course contents

1	Topological Spaces
2	Contininuous Function
3	Differentiable Manifold
4	Differentiable Function
5	The Induced Topology on a Manifold
6	The Induced Topology on a Manifold
7	Differentiable Varieties
8	Manifold Structure on a Topological Space
9	Properties of Induced Topolgy
10	Topological Restrictions on a Manifold
11	Partial Differentiation
12	Tangent Vectors
13	Immersions
14	Submanifolds
15
16
17
18
19
20

Learning outcomes of the course unit

1	To understand topological spaces
2	To understand differential manifolds
3	To understand differantial and continious functions
4	To understand relation bitween differantial monifolds andt topological spaces
5	To understand property of topology of differential manifolds
6	To understand Tanjant Vectors
7
8
9
10

*Contribution level of the course unit to the key learning outcomes

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
Number of stars refer to level of contribution from 1 (the least) to 5 (the most)

Planned learning activities, teaching methods and ECTS work load

	Quantity	Time (hour)	Quantity*Time (hour)
Lectures (face to face teaching)	14	3	42
Study hours out of classroom (study before and after the class)	14	6	84
Homework	0	0	0
Presentation / seminar	0	0	0
Quiz	0	0	0
Preparation for midterm exams	5	4	20
Midterm exams	1	2	2
Project (term paper)	0	0	0
Laboratuar	0	0	0
Field study	0	0	0
Preparation for final exam	5	4	20
Final exam	1	2	2
Research	7	2	14
Total work load			184
ECTS			7.50

Assessment methods and criteria

Evaluation during semester	Quantity	Percentage
Midterm exam	1	100
Quiz	0	0
Homework	0	0
Semester total		100
Contribution ratio of evaluation during semester to success		40
Contribution ratio of final exam to success		60
General total		100

Recommended and required reading

Textbook	Brickell, F., Clark, R. S.,Differentiable Manifolds, Van Nostrand Reinhold Company London, 13-33, 1976.
Additional references	1) Chevalley, C., Theory of Lie Groups, Princeton University Press, 1946. 2) Mackenzie, K., Lie Groupoids and Lie Algebroids in Differential Geometry, London Math. Soc. Lec. Notes Series,Cambridge University Press, 1987.

Files related to the course unit